On a hot day in July, students in Bill Buchanan’s math class at Foreman High School saunter around waving fake hundred-dollar bills. In clusters of four, they play dice and card games. But the main attraction is a roulette-like game. The dealer, senior Lisabelle Valle, instructs all players not to touch the board once their bets are placed. One student, who bet all his money on one number and lost, insists on playing one more round. “What do you have for collateral?” demands Lisabelle.
On the surface it’s play, but underneath it’s the serious business of learning about money, communications and math, especially math. “This whole class flunked during the regular school year, but now they are all passing,” says Buchanan.
Buchanan’s unusual way of teaching math skills is part of a program that just nabbed a $900,000 grant from the National Science Foundation for expansion in the Chicago public schools. Called the Interactive Mathematics Program (IMP), it is a four-year secondary curriculum used in 178 high schools nationwide. IMP was introduced at Lake View High School in 1992, and spread to another 11 high schools over the past five years through the Institute of Math and Science Education at the University of Illinois at Chicago. The new grant will pay for training and support for 200 teachers in 27 schools.
“This is more active learning, not just memorizing formulas,” says institute director Philip Wagreich.
Buchanan says he prefers IMP to a traditional math program because students “are constantly presenting their work to the class, as opposed to just writing it down and handing it in. They learn to defend their ideas.”
No answer book
IMP departs from standard mathematics instruction in several other significant ways. For one, it integrates five core areas—algebra, geometry, trigonometry, statistics and probability—and teaches them simultaneously rather than sequentially. Over time, the lessons become more sophisticated and abstract, building on the skills students already have learned. Further, since the program challenges students to find solutions to real-life problems, there is no answer book for teachers or students.
“To us as math teachers, the most important thing for people to realize is that mathematics is a really powerful tool in solving problems,” says Margaret Small, project co-director. “There’s a certain analytic power to mathematics that’s more than opinion.”
After Lisabelle’s roulette game, Buchanan writes equations showing students how math relates to their probability games. Then students complete a worksheet of five problems based on probability.
As for the gambling part, co-director Anne Horn says, “I believe these probability games teach kids not to gamble. They know what a small chance there is to win at casinos, the race track or even the lottery. The students know this is not a lucrative way to make a living.”
Edgar Allan Poe’s story “The Pit and the Pendulum” provides the springboard for another lesson. Students read an excerpt of the story about a prisoner looking up at a razor-sharp pendulum that threatens to slice him in half. Then comes their challenge: “How much time does the prisoner have to escape?” Students construct their own 30-foot pendulum to test their estimates. In the process, they learn complex mathematical concepts such as standard deviations, normal distributions and functions.
IMP not only has made math more interesting for students, it also has produced gains on basic skills tests. At Lakeview High School, for example, juniors who had taken IMP for three years advanced 2.1 years on the Tests of Achievement and Proficiency between 1995 and 1996. Juniors who had taken traditional math courses advanced 1.5 years.
“There’s a large number of people who agree that what we’re doing in math education needs to change, but how it should change, that always makes people very nervous,” says Small. “One of the reasons U.S. students score lower than other students [on international tests] is that we have a shotgun approach to math in high school.
“We want kids to memorize a million things and test them on it, and nobody remembers anything. Using these new approaches to math instruction is important in Chicago if we are going to successfully have all students pass three years of high school math.”
Beginning with the Class of 2000, which is in its sophomore year, CPS students must take three years of high school math to graduate.
The Reform Board recently approved academic standards that align with state goals; now it is developing end-of-course tests.
Small says IMP covers the state math goals, which include measurement, number sense, geometric thinking, algebraic thinking and probability and statistics. “The end-of-course test will be integrated to test for the five state goals, not strictly algebra or geometry,” she says.
1997-98: Clemente, Chicago Vocational, DuSable, Foreman, Future Commons, Lakeview, Richards, South Shore, Wells, Whitney Young and two charter schools, Acorn and Perspective Academy for Communication and Technology.
1998-99: Bowen, Robeson, Simeon, Corliss, Orr, King and Harper.
For more information:
Philip Wagreich, director of UIC’s Institute for Mathematics and Science Education: (312) 413-3019
Anne Horn, project co-director Chicago IMP: (773) 535-1098
Margaret Small, project co-director Chicago IMP: (312) 996-2448
Interactive Mathematics Program (IMP) Toll-free: 1-888-628-4467
National Science Foundation: (202) 342-2760